Universität Augsburg
Institut für Mathematik

I will explain how to study the space of positive scalar curvature metrics on a given manifold by comparing it with a cubical approximation, called the concordance space of psc metrics. In addition to providing new proofs of earlier detection results concerning the homotopy groups of the space of psc metrics on a compact manifold, we give the first systematic treatment of these spaces when the underlying manifold does not admit a spin structure. The proof works by constructing a comparison map from the positive scalar curvature cobordism category introduced by Ebert--Randal-Williams to a fibration of Quinn's cubical bordism sets, which we enrich with positive scalar curvature metrics.

This is joint work with Thorsten Hertl.